Asymptotic Tracking and Linear-Like Behavior Using Multi-Model Adaptive Control

• 成果类型: Article
• 署名作者: Shahab, Mohamad T.; Miller, Daniel E.
• 署名单位: University of Waterloo; King Abdullah University of Science & Technology
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2021.3052745
• 发表日期: 2022
• 页码: 203-219
• 关键词: adaptive control; bounded noise gain; exponential stability; multiple estimators; switching adaptive control

摘要

In this article, we consider the problem of tracking for a discrete-time plant with unknown plant parameters; we assume knowledge of an upper bound on the plant order, and for each admissible order we assume knowledge of a compact set in which the plant parameters lie. We carry out parameter estimation of an associated auxiliary model; indeed, for each admissible dimension, we cover the set of admissible parameters by a finite number of compact and convex sets and use an original-projection-algorithm-based estimator for each set. At each point in time, we employ a switching algorithm to determine which model and parameter estimates are used in the pole-placement-based control law. We prove that this adaptive controller guarantees desirable linear-like closed-loop behavior: exponential stability, a bounded noise gain in every p-norm, a convolution bound on the effect of the exogenous inputs, as well as exponential tracking for certain classes of reference and noise signals; this linear-like behavior is leveraged to immediately show tolerance to a degree of plant time-variations and unmodeled dynamics.